Stochastic Boundary, Diffusion, Emittance Growth and Lifetime calculation for the RHIC e-lens

To compensate the large tune shift and tune spread generated by the head-on beam-beam interactions in polarized proton operation in the Relativistic Heavy Ion Collider (RHIC), a low energy electron beam with proper Gaussian transverse profiles was proposed to collide head-on with the proton beam. In this article, using a modified version of SixTrack [1], we investigate stability of the single particle in the presence of head-on beam-beam compensation. The Lyapunov exponent and action diffusion are calculated and compared between the cases without and with beam-beam compensation for two different working points and various bunch intensities. Using the action diffusion results the emittance growth rate and lifetime of the proton beam is also estimated for the different scenarios.